Algorithm 1 Mapping from RGB color space to order space

Require:  a set of pixels $\{f_{i+k,j+l}=[f_{i+k,j+l}^{\mathrm{R}},f_{i+k,j+l}^{\mathrm{G}},f_{i+k,j+l}^{\mathrm{B}}]|(k,l)\in S\}$ Ensure:  a set of coordinates in order space $\{(o_{\xi }^{\mathrm{R}},o_{\xi }^{\mathrm{G}},o_{\xi }^{\mathrm{B}})|\xi \in \{1,2,\dots ,\left|S\right|\left\}\right\}$  1:Assign serial numbers $\xi \in \{1,2,\dots ,|S\left|\right\}$ to all pixels in the required set to have a set of re-indexed pixels $\{f_{\xi }=[f_{\xi }^{\mathrm{R}},f_{\xi }^{\mathrm{G}},f_{\xi }^{\mathrm{B}}]|\xi \in \{1,2,\dots ,\left|S\right|\left\}\right\}$.  2:for $\mathrm{X}\in \{\mathrm{R},\mathrm{G},\mathrm{B}\}$ do  3:    $[a_1^{\mathrm{X}},a_2^{\mathrm{X}},\dots ,a_{\left|S\right|}^{\mathrm{X}}]=\mathrm{argsort}(f_1^{\mathrm{X}},f_2^{\mathrm{X}},\dots ,f_{\left|S\right|}^{\mathrm{X}})$  4:    for $\xi \in \{1,2,\dots ,|S\left|\right\}$ do  5:        $o_{a_{\xi }^{\mathrm{X}}}^{\mathrm{X}}=\xi$  6:    end for  7:end for  8:Return $\{(o_{\xi }^{\mathrm{R}},o_{\xi }^{\mathrm{G}},o_{\xi }^{\mathrm{B}})|\xi \in \{1,2,\dots ,\left|S\right|\left\}\right\}$